Related papers: Neumann system and hyperelliptic al functions
In this work we give an explicit solution to the problem of differentiation of hyperelliptic functions in genus $4$ case. It is a genus $4$ analogue of the classical result of F. G. Frobenius and L. Stickelberger [F. G. Frobenius, L.…
The purpose of this material is to review the Adler Kostant Symes scheme as a theory which can be developped succesfully in different contexts. It was useful to describe some mechanical systems, the so called generalized Toda, and now it…
New methods for obtaining functional equations for Feynman integrals are presented. Application of these methods for finding functional equations for various one- and two- loop integrals described in detail. It is shown that with the aid of…
We develop the theory of hyperelliptic Kleinian functions. As applications we consider construction of the explicit matrix realization of the hyperelliptic Kummer varieties, differential operators to have the hyperelliptic curve as spectral…
The problem of determining the mathematical model of the dynamics of multi-dimensional control systems in the presence of noise under the condition that the correlation functions cannot be found. Known statistical dynamics of linear systems…
Classical dynamical equations describing a certain version of the nonHamiltonian interaction of two rotators (Euler tops with completely degenerate inertia tensors) are considered. The simplest case is integrated. It is shown that the…
A procedure is introduced which allows to represent the dynamics of a non-equilibrium system violating detailed balance by its steady state loop fluxes. It is shown that detailed balance is restored in this representation, such that the…
In this article one introduces a formalism of classical mechanics where complex Lagrangian functions are admitted. The results include complex versions of the Lagrangian function, of the Euler-Lagrange equation, of the Hamilton principle, a…
We give a survey on classical and recent applications of dynamical systems to number theoretic problems. In particular, we focus on normal numbers, also including computational aspects. The main result is a sufficient condition for…
The dynamical systems of the form $\ddot\bold r=\bold F (\bold r,\dot\bold r)$ in $\Bbb R^n$ accepting the normal shift are considered. The concept of weak normality for them is introduced. The partial differential equations for the force…
This is an expository plus research paper which mainly exposes preliminary connection and contrast between classical complex dynamics and semigroup dynamics of holomorphic functions. Classically, we expose some existing results of rational…
In this note, we verify that the bounded shadowing property and quasi-hyperbolicity of bounded linear operators on Hilbert spaces are preserved under Aluthge transforms.
We consider dynamical systems associated to Lax pairs depending rationnally on a spectral parameter. We show that we can express the symplectic form in terms of algebro--geometric data provided that the symplectic structure on L is of…
The methods are proposed for evaluation of complex dynamical systems, choice of their optimal operating modes, determination of optimal operating system from given class of equivalent systems, system's timeline behaviour analysis on the…
The Neumann--Neumann method is a commonly employed domain decomposition method for linear elliptic equations. However, the method exhibits slow convergence when applied to semilinear equations and does not seem to converge at all for…
The variational model for a ferroelectric nematic bears close resemblance to the well-known energy model for micromagnetics. Despite this similarity, the two models operate in fundamentally distinct parameter regimes describing different…
Using techniques from geometry and complex analysis in their simplest form, we present a derivation of electric fields on surfaces with non-trivial topology. A byproduct of this analysis is an intuitive visualization of elliptic functions…
Linear finite dynamical systems play an important role, for example, in coding theory and simulations. Methods for analyzing such systems are often restricted to cases in which the system is defined over a field %and usually strive to…
Dynamic properties of fermionic systems, like contollability, reachability, and simulability, are investigated in a general Lie-theoretical frame for quantum systems theory. Observing the parity superselection rule, we treat the fully…
Connections between partial dynamcial systems, a generalized notion of partial dynamical systems defined by nested sequences of partial homeomorphisms, and triangular AF algebras which admit an integer-valued cocycle are established.